AP Physics C: Mechanics 1.5 A Describe the Motion of an Object Moving in Two or Three Dimensions Topic 1 5 Motion in Two or Three Dimensions Questions

Describe multidimensional motion by resolving vectors into independent components and applying constant-acceleration models to trajectories, timing, range, and speed.

Exam points

resolve initial velocity or acceleration into horizontal and vertical components using geometry
apply independent component equations to derive position and velocity as functions of time
determine flight time from vertical motion and horizontal range from constant horizontal velocity
calculate the speed or direction of a projectile at its highest point or at impact
compare projectile trajectories when launch conditions, gravity, release time, or platform motion changes

[Maximum number: 2]

A block of mass m is placed on top of an ideal spring of spring constant k. The block is pushed against the spring, compressing the spring a distance $\Delta x$ . The block is released from rest, leaves the spring at the position shown in the figure, travels upward, and enters a track with a constant radius of curvature R that has negligible friction. The block enters the track at point A, maintains contact with the track, and exits horizontally at point B, a distance 3 R above the point the block was released. The block then falls to the ground and lands a horizontal distance D from the end of the track. Express all algebraic answers in terms of $m, k, \Delta x, R$ , and physical constants, as appropriate. The size of the block is much smaller than the radius of curvature of the track.

Calculate the distance D that the block travels.

For correctly relating the height of fall to the time of fall
$y=y_{0}+v_{o y} t+\frac{1}{2} a_{y} t^{2} \therefore H=0+0+\frac{1}{2} g t^{2} \therefore t=\sqrt{\frac{(2)(4 R)}{g}}=\sqrt{\frac{8 R}{g}}$

1 point

For correctly substituting into the equation for constant velocity consistent with part (b)(i)
$D=v_{x} t=\left(\sqrt{\frac{k}{m}(\Delta x)^{2}-6 g R}\right)\left(\sqrt{\frac{8 R}{g}}\right)$

1 point

Total for part (d)

2 points

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AP Physics C: Mechanics 1.5 A Describe the Motion of an Object Moving in Two or Three Dimensions Topic 1 5 Motion in Two or Three Dimensions Questions question 1